A Novel Bimodal Hydro-Mechanical Coupling Model for Evaluating Rainfall-Induced Unsaturated Slope Stability

Abstract

The soil water characteristic curve (SWCC) is a key foundation in unsaturated soil mechanics describing the relationship between matric suction and water content, which is crucial for studies on effective stress, permeability coefficients, and other soil properties. In natural environments, colluvial and residual soils typically exhibit high pore heterogeneity, and previous studies have shown that the SWCC is closely related to the distribution of pore sizes. The SWCC of soils may display either a unimodal or bimodal distribution, leading to different hydraulic behaviors. Past unsaturated slope stability analyses have used the unimodal SWCC model, but this assumption may result in evaluation errors, affecting the accuracy of seepage and slope stability analyses. This study proposes a novel bimodal hydro-mechanical coupling model to investigate the influence of bimodal SWCC representations on rainfall-induced seepage behavior and stability of unsaturated slopes. By fitting the unimodal and bimodal SWCCs with experimental data, the results show that the bimodal model provides a higher degree of fit and smaller errors, offering a more accurate description of the relationship between matric suction and effective saturation, thus improving the accuracy of soil hydraulic property assessment. Furthermore, the study established a hypothetical slope model and used field data of landslides to simulate the collapse of Babaoliao in Chiayi County, Taiwan. The results show that the bimodal model predicts slope instability 1 to 3 h earlier than the unimodal model, with the rate of change in the safety factor being about 16.6% to 25.1% higher. The research results indicate the superiority of the bimodal model in soils with dual-porosity structures. The bimodal model can improve the accuracy and reliability of slope stability assessments.

1. Introduction

The analysis of slope stability represents a key focus within the field of geotechnical engineering research. In recent years, numerous studies have focused on the analysis and investigation of unsaturated slope stability [1,2,3,4,5,6,7,8,9]. In unsaturated soil mechanics, the soil water characteristic curve (SWCC) serves as a fundamental concept. It describes the relationship between matric suction and water content in soil and significantly influences the soil’s hydraulic and mechanical properties such as permeability, effective stress, and shear strength [10,11,12,13,14,15,16].

The pore structure and pore size distribution (PSD) of soils have a decisive influence on the shape of the SWCC [17,18,19,20,21,22,23]. Soils with uniform or well-graded textures typically exhibit a unimodal pore size distribution, resulting in a more homogeneous pore structure and a smooth, unimodal S-shaped SWCC during drainage. In contrast, soils with a bimodal pore size distribution, such as some colluvial and residual soils [24,25], contain two distinct scales of pores, which can lead to the manifestation of bimodal or even multimodal characteristics in their SWCC. The unimodal and bimodal characteristics of the SWCC are illustrated in Figure 1. Durner’s [26] research indicates that soils with a bimodal pore size distribution may exhibit a bimodal pore structure in the soil particles. Furthermore, existing research indicates that the soil pore size distribution significantly influences unsaturated hydraulic properties and shear strength. The research results by Qian et al. [27] show that compacted soils exhibit a bimodal pattern, influenced by the air-entry value and residual suction, which, in turn, affect the shear strength and permeability of unsaturated soils. Zhou and Chen [28] studied the impact of soil heterogeneity on the SWCC by simplifying soil pores into a series of elliptical shapes. Their findings revealed that soil heterogeneity leads to higher water content being retained at a given suction. Lin, et al. [29] studied the shear strength of unsaturated soils with unimodal and bimodal SWCCs. Their results showed that the bimodal SWCC exhibited a bilinear strength envelope, which was different from the results observed for soils with a unimodal SWCC. Giannini et al. [30] developed a GIS-based tool that enables the calculation of coseismal displacements across large areas while considering the influence of varying soil water saturation on slope slip behavior.

The soil water characteristic curve is obtained through experimental testing or model fitting. The accuracy of the curve fitting can significantly affect hydraulic coupling and the predictions of model simulations. Due to the heterogeneity of soil properties and pore structures, discrepancies may arise between experimental data and the fitted curve. This may indicate that the soil exhibits bimodal or even multimodal hydraulic characteristics. In such cases, using an appropriate hydraulic model can provide a higher-precision fit for the SWCC, thereby enhancing the simulation and estimation of unsaturated soil hydraulic properties and stress distribution. The study by Yeh et al. [31] demonstrated that the fitted SWCC parameters for in situ soils showed better performance and could describe the variations in the hydraulic behavior of dual-porosity soils resulting from rainfall.

Rainfall is one of the primary factors that trigger slope instability [32,33,34,35,36,37,38]. Rainfall-induced landslides are closely related to changes in pore water pressure and infiltration behavior [39]. Therefore, the soil water characteristic curve plays a crucial role in the analysis of unsaturated slope stability. When a rainfall event occurs, the infiltrating rainwater changes the pore water pressure within the unsaturated soil of the slope, reducing the effective stress and consequently decreasing the soil shear strength, which can lead to slope failure [40]. Many past studies have used the SWCC to estimate unsaturated soil hydraulic conductivity and shear strength in order to address issues related to the stability assessment of unsaturated slopes [41,42,43,44,45,46,47]. Lu and Likos [48] proposed the suction stress theory, which uses the SWCC to quantify the influence of matric suction on the effective stress in soil. They derived the suction stress characteristic curve (SSCC), which illustrates the relationship between the effective saturation of the soil and suction stress. This curve is used to calculate the stress state in unsaturated soils. However, previous studies have seldom addressed the effect of rainfall infiltration on the internal hydraulic properties and stress distribution in dual-porosity or multi-porosity soils. This study explores and compares two hydraulic models using the bimodal model to simulate and predict changes in soil water content and stress, as well as to evaluate the stability of unsaturated slopes.

In addition, traditional slope stability analysis often employs the Limit Equilibrium Method (LEM). This method requires assuming the geometry and location of the potential failure surface before analysis, dividing the volume of the potential failure slope into small vertical slices. As a result, it has certain limitations in predicting the initial failure location, occurrence time, and the failure process of the slope [49,50,51,52,53]. Based on the principles of stress or moment equilibrium, the factor of safety (FS) is commonly employed as a critical parameter for evaluating slope stability. However, this method cannot provide insight into the initial failure location or how the potential unstable areas evolve with changes in pore water pressure due to rainfall infiltration. Lu et al. [54] introduced the Local Safety Factor (LFS) theory, which provides an effective method for assessing stability at any location within the slope. This method clearly describes the geometry and timing of the potential failure surface [55], further enhancing the accuracy and practicality of slope stability analysis.

This investigation is focused on evaluating the effects of different SWCC formulations—particularly the bimodal model—on the seepage behavior and stability of rainfall-induced unsaturated slopes within a coupled hydro-mechanical framework. The bimodal SWCC model is employed to simulate moisture migration and changes in shear strength within the slope under rainfall conditions, while the local factor of safety (LFS) theory is applied to assess slope stability. Numerical simulations are conducted using both experimental data from the published literature and field measurements to quantitatively evaluate the influence of various hydraulic models on the stability of unsaturated slopes. The study further explores how differences in hydraulic modeling affect seepage patterns and stress distributions. Additionally, four types of rainfall events are simulated on a typical hypothetical slope to reveal the impacts of different hydraulic models on slope seepage and stability under varying rainfall scenarios.

2. Materials and Methods

2.1. Typical Soil Water Characteristic Curve (SWCC)

In unsaturated soil mechanics, the numerical fitting of the soil water characteristic curve is an important method for studying the relationship between soil water content and matric suction. The SWCC is related to soil structure and pore size distribution. For homogeneous soils with a single pore structure, the SWCC typically displays a unimodal characteristic. This study adopts the closed-form analytical solution proposed by van Genuchten [56], which is a widely used method in unsaturated soil seepage analysis. The model includes four parameters and is used to predict the variation of soil volumetric water content with matric suction. This relationship can be formulated as:

$$\theta (h)={\theta }_r+{\displaystyle \frac{{\theta }_s-{\theta }_r}{{\left[1+\alpha {\left|\left(u_a-u_w\right)\right|}^n\right]}^m}}$$

(1)

where ${\theta }_s$$[-]$ denotes the saturated water content, ${\theta }_r$$[-]$ represents the residual water content, $\left(u_a-u_w\right)$${[\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}]$ represents the matric suction, and $\alpha$$[1/m]$ and $n$$[-]$ are fitting parameters of the SWCC, with $m=1-1/n$.

The permeability of unsaturated soil is influenced by matric suction, resulting in varying hydraulic conductivity under different saturation conditions. The soil’s permeability can be evaluated using the SWCC, which estimates hydraulic conductivity based on changes in soil saturation. In this study, the hydraulic conductivity function (HCF), which varies with effective soil saturation, is calculated based on the model proposed by Mualem [13] and the SWCC. The function is expressed as:

$$K=K_s{S}_e^l{\left[1-{\left(1-S_e^{1/m}\right)}^m\right]}^2$$

(2)

where $K_s$$[L{T}^{-1}]$ denotes the saturated hydraulic conductivity, $l$$[-]$ represents the soil porosity correlation coefficient, and $S_e$$[-]$ indicates the equivalent degree of saturation. The equation is given as follows:

$${\mathrm{S}}_e={\displaystyle \frac{\theta -{\theta }_r}{{\theta }_s-{\theta }_r}}$$

(3)

2.2. Bimodal Soil Water Characteristic Curve (BSWCC)

Due to the influence of soil structure and pore size distribution, the SWCC may exhibit a bimodal curve. When the soil structure contains both macropores (coarse particles) and micropores (fine particles), a dual pore size distribution is formed. The differences in pore size distribution affect the soil’s hydraulic properties, so the evaluation of dual-pore soils cannot be performed using the unimodal SWCC equation. [57]. Therefore, the bimodal SWCC model proposed by Durner [26] is used to fit the field soil data. This function superimposes van Genuchten [56] model curves with assigned weighting factors to describe the SWCC of pore heterogeneity. The bimodal SWCC is given as:

$${\mathrm{S}}_e={\displaystyle \sum _{i=1}^2{w}_i{\left[\frac{1}{1+{\left({\alpha }_i\left|h\right|\right)}^{n_i}}\right]}^{m_i}}$$

(4)

where $h$$\left[\mathrm{L}\right]$ denotes the pressure head or suction head, and $w_i$$[-]$ represents the weighting factor of the single pore domain, with $w_1=1-w_2$.

To identify the optimal parameter combination for the bimodal SWCC model, this study employed the root mean square error (RMSE) as the goodness-of-fit evaluation criterion. The parameters were determined by comparing the errors between the model-predicted curves and the experimental SWCC data.

The hydraulic conductivity function (HCF) is derived based on the SWCC and describes how the hydraulic conductivity changes with variations in the effective saturation of the soil. To describe the hydraulic conductivity of dual-porosity unsaturated soils, the model combines the approaches of Mualem [13] and van Genuchten [56]. The bimodal hydraulic conductivity can be expressed as:

$$\mathrm{K}\left({\mathrm{S}}_e\right)=K\left(h_i\right){\left({\displaystyle \sum _{i=1}^k{w}_i}{S}_{ei}\right)}^{0.5}{\left({\displaystyle \frac{{\displaystyle \sum _{i=1}^k{w}_i{\alpha }_i\left\{1-{\left({\alpha }_{i}h\right)}^{n_i-1}{\left[1+{\left({\alpha }_{i}h\right)}^{n_i}\right]}^{-m_i}\right\}}}{{\displaystyle \sum _{i=1}^k{w}_i{\alpha }_i}}}\right)}^2$$

(5)

where $k$ denotes the mode of the model (i.e., $k=2$, which is a double peak), and $K\left(h_i\right)$ represents the unsaturated hydraulic conductivity function defined by the steady-state flow method at a pressure head of i = −1 kPa.

2.3. Coupled Hydro-Mechanical Framework

In this study, the finite element model HYDRUS 2D, combined with the Slope Cube Module, is employed to simulate the one-way coupled variably saturated flow and stress response, following the analysis procedure illustrated in Figure 2. The model is based on unsaturated flow theory for seepage simulation and utilizes the internal Slope Cube Module to analyze changes in the soil stress field, describing the impact of different hydraulic behaviors on seepage. This model, developed by Simunek et al. [58], is based on the Richards equation and establishes a two-dimensional transient seepage equation for solving the hydraulic properties of unsaturated soil layers. The analytical expression for transient unsaturated flow is given as follows:

$${\displaystyle \frac{\partial \theta \left(h\right)}{\partial t}}=\nabla \cdot K\left(h\right)\nabla H+W$$

(6)

where $\theta \left(h\right)$$[-]$ denotes the volumetric water content corresponding to changes in pore water pressure, $K\left(h\right)$${[\mathrm{LT}}^{-1}]$ represents the hydraulic conductivity term corresponding to changes in pore water pressure, $t$$\left[\mathrm{T}\right]$ represents time, and $W$$[L^3{T}^{-1}]$ represents the seepage caused by infiltration behavior.

The Slope Cube Module employs the FEM2D [59] finite element method to compute the stress distribution within the slope, utilizing the principle of momentum equilibrium. This module simulates stress variations resulting from transient changes in unit weight using the plane stress linear elasticity approach. According to linear elasticity theory, the governing equation for computing the total stress distribution is given by:

$$\nabla \cdot \left(\sigma \right)+\gamma \left(\theta \right)b=0$$

(7)

where $\sigma$ [ML⁻¹T⁻²] denotes the independent stress variable in two-dimensional space, $\gamma \left(\theta \right)$ represents the unit weight of soil subject to changes in water content, and b indicates the unit vector of the body force.

2.4. Concept of Effective Stress in Unsaturated Soils

This study adopts the effective stress theory proposed by Terzaghi [60] and incorporates the modification introduced by Bishop [61], which accounts for the influence of capillary effects in unsaturated soils. The effective stress is expressed as:

$$\sigma \prime =\sigma -u_a-{\sigma }^s$$

(8)

where ${\sigma }^{\prime }$ $[M{L}^{-1}{L}^{-2}]$ denotes the effective stress, $\sigma$ $[M{L}^{-1}{L}^{-2}]$ represents the total stress, $u_a$ $[M{L}^{-1}{L}^{-2}]$ represents the pore air pressure, and ${\sigma }^s$ [ML⁻¹T⁻²] represents the suction stress.

Due to the relatively small magnitude of physico-chemical forces, they can be considered negligible. Therefore, the soil stress components can be expressed as a function of degree of saturation or water content and matric suction. Lu, Godt, and Wu [11], based on thermodynamic principles, interpreted suction stress as the energy stored in a unit volume of soil and developed the suction stress characteristic curve (SSCC) from the SWCC. The analytical expression is given as follows:

$${\sigma }^s=-S_e(u_a-u_w)=-{\displaystyle \frac{\left(u_a-u_w\right)}{{\left\{1+{\left[\alpha \left(u_a-u_w\right)\right]}^n\right\}}^{(n-1)/n}}}$$

(9)

where $u_w$$[M{L}^{-1}{L}^{-2}]$ is the water pressure.

Since the SSCC is derived from the soil water characteristic curve (SWCC), the SSCC calculated using a bimodal SWCC also exhibits bimodal behavior. Based on the bimodal saturation equation proposed by Durner [26], substituting Equation (4) into the analytical expression for the SSCC proposed by Lu, Godt, and Wu [11] allows for the bimodal suction stress to be expressed in the following form:

$${\sigma }^s=-{\displaystyle \sum _{i=1}^2{w}_i\frac{\left(u_a-u_w\right)}{{\left\{1+{\left[{\alpha }_i\left(u_a-u_w\right)\right]}^{n_i}\right\}}^{m_i}}}$$

(10)

2.5. Local Factor of Safety (LFS)

This study employs the local factor of safety (LFS) theory to assess slope stability. By integrating this theoretical framework with the finite element method, soil stability can be evaluated at various locations and depths within the slope, while also considering the impact of water content changes and suction stress on stability. Proposed by Lu, Şener-Kaya, Wayllace, and Godt [54], the LFS theory builds upon the Mohr–Coulomb failure criterion and defines the local factor of safety as the ratio between the potential Coulomb stress and the current Coulomb stress. Translating Mohr’s circle representing the current stress state to the failure envelope allows for the calculation of the shear stress at failure, i.e., the potential Coulomb stress. This resembles the condition in which an increase in water content reduces the effective stress, resulting in Mohr’s circle shifting to the left. Since the total stress in the soil is primarily influenced by the unit weight of the soil material and the geometry of the slope, the size of Mohr’s circle remains relatively constant during this translation. A conceptual diagram of this theory is shown in Figure 3, and the LFS is defined as follows:

$$LFS={\displaystyle \frac{\tau *}{\tau }}={\displaystyle \frac{\cos \phi \prime }{{\sigma }_1-{\sigma }_3}}[2c\prime +({\sigma }_1+{\sigma }_3-2{\sigma }^s)\tan \phi \prime ]$$

(11)

where $\tau *$$[M{L}^{-1}{L}^{-2}]$ denotes the shear strength, also referred to as the potential Coulomb stress, $\tau$$[M{L}^{-1}{L}^{-2}]$ represents the shear stress, also referred to as the current Coulomb stress, $c^{\prime }$ is the effective cohesion of the soil, ${\phi }^{\prime }$ is the effective friction angle of the soil, ${\sigma }_1^{\prime }$ and ${\sigma }_3^{\prime }$ represent the maximum and minimum effective stresses of the soil, respectively.

3. Results

3.1. Comparative Analysis of Unimodal and Bimodal Soil Water Charateristic Curve Models

This study aims to verify that the bimodal model more accurately describes the hydraulic characteristics of soils with dual-porosity media and to compare and analyze the SWCC model using a representative soil sample. This section presents a comparison and analysis of the SWCC model, based on experimental data from previous studies by Lin, Qian, Shi, and Zhai [29] and Chen and Feng [62]. The fitting was performed using Equations (1) and (4), respectively. The soil sample was K10S90, which is classified as SP according to the Unified Soil Classification System (USCS). This soil is made by mixing 10% kaolin and 90% standard sand, and its particle size distribution exhibits a gap-grading, making it suitable as a representative of soils with dual-porosity characteristics. Nanyang clay is a common type of clay found in Singapore, characterized by dual porosity.

Therefore, this soil was selected for comparative analysis in the study. As can be seen from Figure 4, for both soil samples, the bimodal model has a better fit to the experimental data than the unimodal model. The fitting results were evaluated using the root mean square error (RMSE) to assess the fitting accuracy. The RMSE values for the unimodal model were 0.0631 and 0.1218, respectively, while the RMSE values for the bimodal model were 0.0185 and 0.0265. The results show that the bimodal model provides a better fit, indicating that it offers more accurate evaluation of the hydraulic characteristics for both soil samples.

In addition, it can be observed that the bimodal model curve clearly describes the relationship between soil matric suction and effective saturation. When the effective saturation of the soil reaches a specific range, even small changes in water content can lead to significant changes in matric suction, indicating a high sensitivity to matric suction variations. However, the unimodal model curve only roughly describes the relationship between saturation and matric suction changes, leading to underestimation or overestimation of matric suction changes within certain water content ranges, thereby affecting the accuracy of hydraulic characteristic assessments.

3.2. The Influence of Bimodal SWCC Models on SSCC

The suction stress characteristic curve (SSCC) describes the relationship between soil suction stress and moisture content, revealing the influence of water content on soil pore water pressure. The SSCC allows for the estimation of stress variations in soils under different water content conditions, which influence the shear strength and deformation behavior of unsaturated soils. Therefore, selecting an accurate SWCC model is crucial for the reliable prediction of the suction stress characteristic curve.

The SSCC results estimated using the two models are shown in Figure 5. It can be observed that the SSCC derived from the bimodal model also exhibits a bimodal characteristic, indicating that suction stress is influenced by the choice of SWCC model. Moreover, it can be observed that the bimodal characteristics vary across different soil types. Influenced by pore size distribution and soil composition, the bimodal SSCC for the K10S90 sample shows relatively limited variation, with changes primarily occurring in the low-suction-stress range. In contrast, the bimodal SSCC for the Nanyang clay exhibits a wider variation range, encompassing both high- and low-suction-stress regions. In all cases, the suction stress variations estimated using the bimodal model differ significantly from those obtained with the unimodal model.

The results estimated using the bimodal model reveal that when the effective degree of saturation of the soil reaches a certain range, even a slight change in water content can lead to a significant variation in suction stress. This phenomenon is consistent with the behavior observed in the SWCC discussed in the previous section, indicating a high sensitivity of suction stress to changes in water content. The hydraulic characteristics estimated by the two models exhibit significant differences, resulting in the unimodal model either underestimating or overestimating suction stress changes at specific water contents. This discrepancy subsequently affects pore water pressure and effective stress, which, in turn, impacts the accuracy of unsaturated slope stability analysis. Therefore, selecting an appropriate SWCC model is crucial for accurately evaluating the mechanical behavior of unsaturated soils and ensuring reliable engineering applications.

3.3. Fitting Results of Soil Hydraulic Parameters

The soil materials used in this study were obtained from field samples of the Babao Liao landslide area. The soil water content and matric suction were determined through laboratory pressure plate tests. Based on the test data, both the unimodal and bimodal SWCC were fitted and compared. The fitting parameters for the single-peak and bimodal SWCC obtained using Equations (1) and (4) are shown in

Table 1. Unimodal soil characteristic curve parameters.

Material	${\mathit{\theta }}_{\mathit{s}}$$[-]$	${\mathit{\theta }}_{\mathit{r}}$$[-]$	$\mathit{\alpha }$$[1/\mathit{m}]$	$\mathit{n}$$[-]$	${\mathit{K}}_{\mathit{s}}\left[\mathit{m}/\mathit{h}\mathit{r}\right]$
Colluvium	0.467	0.031	3.64	1.121	0.00626

and

Table 2. Bimodal soil characteristic curve parameters.

Material	${\mathit{\theta }}_{\mathit{s}}$ $[-]$	${\mathit{\theta }}_{\mathit{r}}$ $[-]$	${\mathit{\alpha }}_1$ $[1/\mathit{m}]$	${\mathit{n}}_1$ $[-]$	${\mathit{w}}_1$ $[-]$	${\mathit{\alpha }}_2$ $[1/\mathit{m}]$	${\mathit{n}}_2$ $[-]$	${\mathit{K}}_{\mathit{s}}$ $\left[\mathit{m}/\mathit{h}\mathit{r}\right]$
Colluvium	0.467	0.031	2.08	1.461	0.46	0.0062	1.798	0.00626

, respectively. The fitting results for both models were evaluated using the RMSE. The RMSE values for the unimodal and bimodal models are 0.0078 and 0.0052, respectively. The results indicate that the bimodal model provides a better fit.

Figure 6a shows the fitting results of the unimodal and bimodal soil water retention curves for the colluvial soil. The figure demonstrates that the bimodal model can fully fit the field material test data and clearly presents the bimodal characteristics. In this study, given the same soil saturation, the unsaturated soil hydraulic conductivity for the unimodal and bimodal models are estimated using Equations (2) and (5), respectively. Due to the influence of different pore structures, the hydraulic conductivity in different pore size regions differs in the bimodal model, leading to variations in hydraulic conductivity between the two hydraulic models. As shown in Figure 6b, the bimodal model exhibits higher hydraulic conductivity, which, in turn, affects the infiltration and stability analysis of unsaturated slope soils.

4. Discussions

4.1. Effect of Different Rainfall Types on the Analysis of Unimodal and Bimodal Models

This section utilizes a finite element analysis model to evaluate the seepage process in unsaturated soils, aiming to examine how unimodal and bimodal hydraulic properties influence slope seepage behavior and stability. A conceptual slope model was developed to simulate and compare the analytical results of both models under different rainfall patterns. A schematic diagram of the model is shown in Figure 7. The slope is assumed to be a typical finite slope with a 30-degree incline. The soil material parameters are based on in situ colluvial soil. According to the USCS, the soil is classified as low-plasticity clay (CL).

Table 3. Soil mechanical parameters.

Material	${\mathit{G}}_{\mathit{s}}$$[-]$	${\mathit{\varphi }}^{\prime }$$[°]$	${\mathit{c}}^{\prime }$$[\mathit{k}\mathit{P}\mathit{a}]$	$\mathit{v}$$[-]$	$\mathit{E}$$[\mathit{k}\mathit{P}\mathit{a}]$
Colluvium	2.62	27	5	0.33	40,000

provides a detailed summary of the mechanical parameters.

The hydraulic boundary conditions of the slope model include an atmospheric boundary at the slope surface, with all other boundaries set as no-flow boundaries. Additionally, an observation profile with a depth of 5 m is set at the center of the slope surface for monitoring and analysis. The mechanical boundary conditions are defined as follows: the slope surface is treated as a free-displacement boundary, while the model’s base is constrained with no displacement along the z-axis. Additionally, zero displacement is applied along the x-axis at both the left and right boundaries. The mesh consists of 1459 nodes and 2784 elements.

In this study, four different rainfall patterns are considered: uniform, advance, delayed, and normal rainfall distributions. The detailed variation of rainfall intensity for each type is shown in Figure 8. A 24 h rainfall event is used as the model input for numerical simulation to analyze the soil water retention curve models of soils with different pore structures under various rainfall patterns and to compare their effects on slope seepage and stability.

4.2. Evaluation of Seepage in Unimodal and Bimodal Models

This section conducts seepage analysis using soil water retention curves from two different models, aiming to explore how variations in internal water content under different rainfall conditions affect pore water pressure within the slope.

The pore structure of soil determines the mechanism of water movement. According to capillarity, different pore sizes correspond to different matric suctions. Micropores, which have higher suction, are able to retain more water, while macropores, with lower suction, have a lower water retention capacity. The heterogeneity of the pores causes the soil moisture to exhibit a staged process during absorption and drainage. Liu et al. [63] show that during the drying process, soil water drains from larger pores first, whereas during the wetting process, the opposite occurs. Therefore, when rainfall infiltration occurs, the micropores are first gradually filled with water, followed by the macropores with lower suction. This two-stage moisture migration behavior leads to a two-stage rapid increase in the pressure head, which will affect the changes in pore water pressure and shear strength.

The variation in the pressure head over time at a depth of 0.5 m under the influence of different rainfall types for the unimodal and bimodal models is shown in Figure 9. From the figure, it can be observed that the initial pressure head for both models is −37.66 m. After infiltration from different rainfall types, the pressure head decline times differ between the two models. After 24 h of rainfall, the pressure head for both models eventually drops to 0 m.

Figure 10 presents the temporal evolution of the soil water content for both the unimodal and bimodal models subjected to different rainfall patterns. Due to the use of different SWCC models, even at the same matric suction, there are still differences in the estimated water content. From the figure, it can be observed that the initial water content for the simulations is 0.271 and 0.286, and after 24 h of rainfall, both models eventually reach a saturated state.

However, due to the influence of different rainfall types, the matric suction estimated by the unimodal and bimodal models differs, resulting in significant variations in the trend of water content changes over time. The pressure head and water content in the unimodal model change more rapidly in a short period, reflecting its quick response to rainfall infiltration. In contrast, the bimodal model shows a more gradual change over time, indicating that the multi-porosity structure influences water movement, allowing it to gradually reach saturation over a longer period.

The results above show that because the bimodal model clearly describes the migration of water in both small and large pores, with micropores having higher suction and being able to retain more water, the simulated matric suction and water content are higher than in the unimodal model. This influences both the timing and the amplitude of their changes, with the differences between the delayed rainfall and normal rainfall being more pronounced. Using the unimodal model, which treats the soil as a single pore structure, fails to effectively reflect the changes in matric suction and water content.

The bimodal model, influenced by the water retention capacity of small pores, shows a higher water content during rainfall compared to the unimodal model. Moreover, the pore structure continues to affect the water retention, causing the changes to occur earlier than in the unimodal model. Accordingly, at the same time, the simulated pressure head values obtained from the bimodal model are higher than those from the unimodal model. The variation in different rainfall patterns also shows differences. If the model is assumed to have a single pore size (i.e., unimodal model), it will fail to accurately simulate the seepage behavior of soils with a multi-pore structure, leading to discrepancies in the pressure head and water content changes over time. Therefore, the analysis should utilize the bimodal model, which accounts for the pore distribution. This model clearly describes the changes in soil water content and matric suction, thus improving the accuracy of the analysis.

4.3. Slope Stability: Unimodal and Bimodal

Through seepage analysis, the internal distribution of the pressure head and soil water content within the slope can be obtained. This allows for the calculation of pore water pressure variations and the stress distribution, which are then used to evaluate their impact on slope stability. Since variations in pore water pressure affect the effective stress in soil and consequently alter its shear strength, this section utilizes the values obtained from the previous analysis to investigate the relationship among the SWCC model, suction stress, and the factor of safety in order to assess changes in slope stability. During rainfall infiltration, the rise in the pressure head and increase in water content lead to a reduction in suction stress. As a result of the changes in pore water pressure, the effective stress in the soil decreases, which lowers the local factor of safety and increases the risk of sliding or failure.

The variation in matric suction and water content further influences the internal stress distribution within the soil. Suction stress represents the equivalent isotropic material stress of the representative volume element consisting of the soil–water–air mixture. The magnitude of interparticle stress changes with particle size and varies in form accordingly [48,64]. Suction stress is a function of the relationship between matric suction and degree of saturation. It is influenced by the interparticle suction and surface tension or capillary effects arising from the negative pore water pressure within the soil matrix.

As the pressure head in the soil increases, the suction stress correspondingly decreases. Therefore, when the soil exhibits a dual-porosity structure, both the SWCC and the SSCC display bimodal characteristics, as illustrated in Figure 11. The figure shows that when the soil has a low degree of saturation, the suction stress estimated using the bimodal model is less sensitive to changes in water content compared to the unimodal model, resulting in significant differences in the estimated suction stress. When the saturation ranges from 0.5 to 1, minor discrepancies between the bimodal and unimodal estimates can still be observed.

As discussed in Section 3.2, within certain saturation intervals, even slight changes in water content can lead to substantial variations in suction stress. This may introduce errors in calculating the soil’s effective stress, potentially compromising the accuracy of slope stability assessments.

Due to the influence of the soil pore structure, in the dual-permeability model, water first fills the micropores when the soil is at a low degree of saturation. At this stage, the pressure head in the soil begins to rise, and the suction stress starts to decrease in the first stage. Once the micropores are saturated, water begins to fill the macropores. Due to the difference in pore sizes, a second significant increase in pressure head occurs, resulting in a second stage of suction stress reduction.

The dual-porosity structure leads to more pronounced variations in the pressure head, causing two distinct phases of suction stress reduction at different water content levels. This alters the internal stress distribution of the soil, affecting both the timing and magnitude of stress changes. The variation in suction stress over time is shown in Figure 12. Taking the advanced rainfall pattern as an example, the suction stress in the unimodal model begins to decrease rapidly from the 2nd hour after the onset of rainfall, reaching its minimum value of −2.26 kPa at the 24th hour. In contrast, the suction stress in the bimodal model starts to decrease earlier, from the 1st hour, and reaches a lower minimum value of −3.37 kPa at the 24th hour. Similar trends are observed under other rainfall patterns.

These results indicate that the heterogeneity of the soil pore structure leads to significant differences in hydraulic characteristics, which, in turn, affect the variation in suction stress. As a result, there are noticeable differences in the timing of the suction stress changes under the different hydraulic models.

The variation of the Local Factor of Safety (LFS) over time at a depth of 0.5 m for both the unimodal and bimodal models under different rainfall patterns is shown in Figure 13. The results reveal a clear discrepancy in the estimated timing of slope instability (LFS < 1) between the two models. Specifically, the bimodal model generally predicts the onset of slope instability 1 to 3 h earlier than the unimodal model. This approach can effectively enhance early warning capabilities, enabling the initiation of emergency measures in advance and significantly improving disaster mitigation outcomes. In practice, a prediction window of 1–3 h allows engineering teams sufficient time to assess and implement intervention strategies, such as increasing monitoring density to track changes in deformation rates.

The analysis of the impact of different rainfall patterns reveals that the frontal rainfall pattern leads to slope instability the earliest, making it the most unfavorable scenario among the four rainfall patterns. The uniform and typical rainfall patterns result in slope instability slightly later than the frontal rainfall. The delayed rainfall pattern, due to its later onset, causes slope instability last among the four types and leaves the slope in an unstable state (i.e., safety factor less than 1) by the end of the rainfall. The initial safety factor values for the two models are 5.42 and 5.66, respectively. Taking the frontal rainfall event as an example, the unimodal model shows a safety factor of 1.61 at the fourth hour, indicating that the slope remains stable. However, the bimodal model shows that the slope has already entered an unstable state at the fourth hour (safety factor of 0.66). Similar trends are observed for other rainfall patterns.

A comparison of the changes in the safety factor over time in the two models is shown in Figure 14. The safety factor change rate for the bimodal model is significantly higher than that of the unimodal model, with a difference ranging from 16.6% to 25.1%. This indicates that there are significant differences between the analysis results of the bimodal and unimodal models. Regardless of the rainfall pattern, the bimodal model consistently predicts the onset of slope instability earlier than the unimodal model.

The above phenomenon is closely related to the characteristics of the hydraulic models. The bimodal SWCC fits the experimental data better than the unimodal model. Compared to the unimodal model, the bimodal model more clearly reflects the soil’s hydraulic properties. Additionally, the estimated hydraulic conductivity function value is higher in the bimodal model, leading to a faster rate of water infiltration in the soil.

As a result, the timing of the safety factor changes evaluated by the bimodal model occurs earlier than in the unimodal model. The differences in the soil water characteristic curve models affect the seepage and stability of unsaturated slopes, emphasizing the critical importance of considering hydraulic models in slope seepage and stability analysis.

5. Conclusions

This study developed a novel bimodal hydraulic coupling model that addresses the limitations of conventional models in representing the SWCC for soils with dual-porosity structures. The soil water characteristic curve (SWCC) was fitted for soils with dual-porosity structures, and the seepage and stability of unsaturated slopes were simulated.

The results indicate that the bimodal model achieves higher fitting precision and reduced error relative to the unimodal model. It more effectively characterizes the linkage between matric suction and soil saturation, thereby improving the reliability of hydraulic property evaluations. There are obvious differences in the hydraulic characteristics estimated by the two models. Particularly within specific ranges of water content, it may lead to overestimation or underestimation of pore water pressure and effective stress, thereby affecting the results of slope stability assessments.

This phenomenon arises from the bimodal model’s enhanced ability to characterize variations in hydraulic conductivity, resulting in greater predicted conductivity values and consequently causing discrepancies in the analysis outcomes between the models. In addition, slope model simulations revealed that the bimodal model performs excellently in fitting the SWCC of field colluvial soils. The simulation results are more consistent with field observations, demonstrating the reliability and accuracy of its application to soils with porous structures.

In summary, when the soil at a research or engineering site exhibits distinct dual-porosity characteristics, the bimodal SWCC model should be employed for simulation and stability analysis. This approach can more accurately reflect the soil’s hydraulic behaviour, thereby improving the precision of simulation and analysis results and ultimately enhancing early warning capabilities.

Future research could further employ experimental methods such as grain size distribution (GSD) analysis and scanning electron microscopy (SEM) to investigate and quantify the influence of soil pore structure on its hydraulic properties. This would contribute to a more precise understanding of the effects of soil pore architecture on hydraulic behaviour, thereby providing more accurate hydraulic parameters for slope stability analysis and enhancing the accuracy and reliability of simulation results.